Agitator mills of this kind, disclosed in U.S. Pat. No. 3,780,957), have circular-cylindrical screen cartridges. They have long since proved to be extraordinarily reliable in use and to have a wide range of applications, because the screen cartridges are readily interchangeable. In practice, however, it has proved disadvantageous that, particularly when the material to be ground is highly viscous, the grinding output of such an agitator mill drops, and the grinding stock becomes heated to an unacceptable extent. At the same time, the auxiliary grinding elements undergo increased breakage. In such agitator mills, the auxiliary grinding elements typically are of glass, sintered Al.sub.2 O.sub.3 or zirconium oxide. Comparable problems arise when low-viscosity material is to be ground if the throughput capacity is to be increased sharply, that is, if there is a throughput of relatively large quantities per unit of time. In addition to the above problems, complete blockage of the agitator mill occurs frequently, so that practically no throughput is accomplished.